NEW ORLEANS, Louisiana (CNN) -- A justice of the peace in Louisiana who has drawn widespread criticism for refusing to issue a marriage license to an interracial couple says he has no regrets about his decision.

Keith Bardwell says he has no regrets for denying a marriage license to an interracial couple.

"It's kind of hard to apologize for something that you really and truly feel down in your heart you haven't done wrong," Keith Bardwell told CNN affiliate WAFB on Saturday.

Bardwell, a justice of the peace for Tangipahoa Parish's 8th Ward, refused to issue a marriage license to Beth Humphrey, 30, and her boyfriend, Terence McKay, 32, both of Hammond.

Bardwell's actions have elicited reactions from some top officials, including Louisiana Gov. Bobby Jindal, who called for Bardwell's dismissal.

"This is a clear violation of constitutional rights and federal and state law. ... disciplinary action should be taken immediately -- including the revoking of his license," the Republican governor said Friday.

Bardwell has not returned repeated calls from CNN this week. But he told Hammond's Daily Star in a story Thursday that he did not marry the couple because he was concerned for the children who might be born of the relationship and that, in his experience, most interracial marriages don't last.

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"I'm not a racist," Bardwell told the newspaper. "I do ceremonies for black couples right here in my house. My main concern is for the children." Bardwell, stressing that he couldn't personally endorse the marriage, said his wife referred the couple to another justice of the peace. Watch why justice says he nixed interracial marriage »

Humphrey and McKay received their marriage license October 9 from another justice of the peace in the same parish. They have reached out to an attorney to determine their next step, Humphrey said.

"We would like him to resign," Beth McKay said. "He doesn't believe he's being racist, but it is racist."

The National Urban League called for an investigation into the incident by the U.S. Justice Department's Civil Rights Division, saying in a statement that Bardwell's actions were "a huge step backward in social justice."

According to the Census Bureau, Tangipahoa Parish is about 70 percent white and 30 percent black.

The U.S. Supreme Court tossed out any racially-based limitations on marriage in the landmark 1967 Loving v. Virginia case. In the unanimous decision, the court said that "Under our Constitution, the freedom to marry, or not marry, a person of another race resides with the individual and cannot be infringed by the State."